Finite Group Databasebeta

← C2×#10607050 #12266753

Subgroups — C2×#10607050 #12266753

Order 1280.

4002 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4040C211yesmaximal, characteristic, complemented
2C22×#4041C211yesmaximal, characteristic
3C22×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C22×C4×D20C211yesmaximal, characteristic, complemented
5C2×C5×#387C211yesmaximal, characteristic, complemented
6C2×#65272C211yesmaximal, characteristic, complemented
7C2×#65229C211yesmaximal, characteristic, complemented
8#10607050C2116yesmaximal, direct product factor
9C2×#64966C211yesmaximal, characteristic, complemented
10C2×#64954C211yesmaximal, characteristic, complemented
11C2×#64954C211yesmaximal, characteristic, complemented
12C2×#64954C211yesmaximal, characteristic, complemented
13C2×#64957C211yesmaximal, characteristic, complemented
14C2×#64957C211yesmaximal, characteristic, complemented
15C2×#64963C211yesmaximal, characteristic, complemented
16C2×#64961C211yesmaximal, characteristic, complemented
17C23×D20C2211yescharacteristic
18C23×D20C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C23×C4×D5C2211yescharacteristic
22C23×C4×D5C2211yescharacteristic
23C23×C4×D5C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C42×C5C2211yescharacteristic
27C22×#685C2211yescharacteristic
28C22×#685C2211yescharacteristic
29C22×#685C2211yescharacteristic
30C22×#685C2211yescharacteristic
31C22×#685C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×C4⋊Dic5C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C2×#4041—28no—
45C2×#4041C2218yes—
46C2×#4040—28no—
47C2×#4040C2218yescomplemented
48C2×D5×C4⋊C4—28no—
49C2×D5×C4⋊C4C2218yescomplemented
50C2×C4×D20—28no—
51C2×C4×D20C2218yescomplemented
52C5×#387C2218yescomplemented
53C2×C5×#95C2211yescharacteristic
54C2×C5×#95C2211yescharacteristic
55C2×C5×#95C2211yescharacteristic
56C2×C5×#95C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60C2×#3963C2211yescharacteristic
61#65272C2218yescomplemented
62#65229C2218yescomplemented
63#64966C2218yescomplemented
64#64963C2218yescomplemented
65#64961C2218yescomplemented
66#64957C2218yescomplemented
67#64957C2218yescomplemented
68#64954C2218yescomplemented
69#64954C2218yescomplemented
70#64954C2218yescomplemented
71C2×#2443—51nomaximal, Sylow
72C24×D5C2311yescharacteristic
73C24×D5C2311yescharacteristic
74C24×D5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C23×C4×C5C2311yescharacteristic
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×Dic5C2311yescharacteristic
83C23×Dic5C2311yescharacteristic
84C23×Dic5C2311yescharacteristic
85C23×Dic5C2311yescharacteristic
86C23×Dic5C2311yescharacteristic
87C22×D20—24no—
88C22×D20—24no—
89C22×D20—24no—
90C22×D20—24no—
91C22×D20—24no—
92C22×D20—24no—
93C22×D20—24no—
94C22×D20—42no—
95C22×D20D418yes—
96C22×D20C2314yes—
97C22×D20C2314yes—
98C22×D20C2314yes—
99C22×C4×D5—24no—
100C22×C4×D5—24no—
101C22×C4×D5—24no—
102C22×C4×D5—24no—
103C22×C4×D5—24no—
104C22×C4×D5—24no—
105C22×C4×D5—24no—
106C22×C4×D5—24no—
107C22×C4×D5—24no—
108C22×C4×D5—42no—
109C22×C4×D5—42no—
110C22×C4×D5—42no—
111C22×C4×D5C2314yes—
112C22×C4×D5C2314yes—
113C22×C4×D5C2314yes—
114C22×C4×D5C2314yes—
115C2×C5×C4⋊C4—24no—
116C2×C5×C4⋊C4D418yescomplemented
117C2×C5×C4⋊C4C2314yes—
118C2×C5×C4⋊C4C2314yes—
119C2×C42×C5—24no—
120C2×C42×C5C2314yes—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—24no—
129C2×#685—24no—
130C2×#685—24no—
131C2×#685—42no—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×#685C2314yes—
139C2×#685C2314yes—
140C2×#685C2314yes—
141C2×#685C2314yes—
142C2×#685C2314yes—
143C2×C4⋊Dic5—24no—
144C2×C4⋊Dic5—24no—
145C2×C4⋊Dic5—42no—
146C2×C4⋊Dic5C2314yes—
147C2×C4⋊Dic5C2314yes—
148C2×C4⋊Dic5C2314yes—
149C2×#683—24no—
150C2×#683—24no—
151C2×#683—24no—
152C2×#683C2314yes—
153C2×#683C2314yes—
154C2×#683C2314yes—
155#4041—232no—
156#4040—232no—
157D5×C4⋊C4—232no—
158C4×D20—232no—
159C5×#95C2314yes—
160C5×#95C2314yes—
161C5×#95C2314yes—
162C5×#95C2314yes—
163#3963C2314yes—
164#3963C2314yes—
165#3963C2314yes—
166#3963C2314yes—
167C22×#123—51no—
168C22×#121—51no—
169C22×C4×D4—51no—
170C23×C4⋊C4—51no—
171#2443—516no—
172C2×#399—51no—
173C2×#398—51no—
174C2×#397—51no—
175C2×#394—51no—
176C2×#388—51no—
177C2×#387D511yescharacteristic, complemented
178C2×#386—51no—
179C2×#386—51no—
180C2×#386—51no—
181C2×#385—51no—
182C2×#385—51no—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5—22no—
200C23×D5—22no—
201C23×D5C2×D414yes—
202C23×D5C2×D414yes—
203C23×D5#4114yes—
204C23×D5#4114yes—
205C23×D5C2412yes—
206C23×D5C2412yes—
207C23×D5C2412yes—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5—22no—
224C22×C4×C5—22no—
225C22×C4×C5C2×D414yes—
226C22×C4×C5C2×D414yes—
227C22×C4×C5C2×D414yes—
228C22×C4×C5C2×D414yes—
229C22×C4×C5C2412yes—
230C22×C4×C5C2412yes—
231C22×C4×C5C2412yes—
232C22×C4×C5C2412yes—
233C22×C4×C5C2412yes—
234C22×C4×C5C2412yes—
235C22×C4×C5C2412yes—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5#4114yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—232no—
257C2×D20—28no—
258C2×D20—28no—
259C2×D20—28no—
260C2×D20—28no—
261C2×D20—28no—
262C2×D20—28no—
263C2×D20—28no—
264C2×D20—44no—
265C2×D20—416no—
266C2×D20—416no—
267C2×D20C2×D4116yes—
268C2×C4×D5—232no—
269C2×C4×D5—28no—
270C2×C4×D5—28no—
271C2×C4×D5—28no—
272C2×C4×D5—28no—
273C2×C4×D5—28no—
274C2×C4×D5—28no—
275C2×C4×D5—28no—
276C2×C4×D5—28no—
277C2×C4×D5—28no—
278C2×C4×D5—44no—
279C2×C4×D5—44no—
280C2×C4×D5—44no—
281C2×C4×D5—416no—
282C2×C4×D5—416no—
283C2×C4×D5—416no—
284C5×C4⋊C4—28no—
285C5×C4⋊C4C2×D4116yescomplemented
286C42×C5—28no—
287#685—28no—
288#685—28no—
289#685—28no—
290#685—28no—
291#685—28no—
292#685—28no—
293#685—28no—
294#685—28no—
295#685—28no—
296#685—28no—
297#685—44no—
298C4⋊Dic5—28no—
299C4⋊Dic5—28no—
300C4⋊Dic5—44no—
301#683—28no—
302#683—28no—
303#683—28no—
304C23×D4—51no—
305C23×D4—51no—
306C23×D4—51no—
307C24×C4—51no—
308C24×C4—51no—
309C24×C4—51no—
310C24×C4—51no—
311C2×#123—58no—
312C2×#123—108no—
313C2×#121—58no—
314C2×#121—108no—
315C2×C4×D4—58no—
316C2×C4×D4—108no—
317C22×C4⋊C4—51no—
318C22×C4⋊C4—51no—
319C22×C4⋊C4—51no—
320C22×C4⋊C4—51no—
321C22×C4⋊C4—51no—
322C22×C4⋊C4—51no—
323C22×C4⋊C4—58no—
324C22×C4⋊C4—108no—
325C22×C4⋊C4C2×D511yescharacteristic
326C22×C4⋊C4C2×D511yescharacteristic
327C22×C22⋊C4—51no—
328C22×C22⋊C4—51no—
329C22×C22⋊C4—51no—
330C22×C22⋊C4—51no—
331C22×C22⋊C4—51no—
332C22×C22⋊C4—51no—
333C22×C22⋊C4—51no—
334C22×C22⋊C4—51no—
335C22×C22⋊C4—51no—
336C22×C22⋊C4—51no—
337C22×C22⋊C4—51no—
338C22×C42C2×D511yescharacteristic
339#399—58no—
340#398—58no—
341#397—58no—
342#394—58no—
343#388—58no—
344#387C2×D518yescomplemented
345#386—58no—
346#386—58no—
347#386—58no—
348#385—58no—
349#385—58no—
350C2×#95—51no—
351C2×#95—51no—
352C2×#95—51no—
353C2×#95—51no—
354C2×#95C2×D511yescharacteristic
355C2×#95C2×D511yescharacteristic
356C2×#95C2×D511yescharacteristic
357C2×#95C2×D511yescharacteristic
358C23×C5C22×D412yes—
359C23×C5C22×D412yes—
360C23×C5C2×#4112yes—
361C23×C5C2×#4112yes—
362C23×C5C2×#4112yes—
363C23×C5H(5,𝔽2)12yes—
364C23×C52−1+412yes—
365C23×C5C2511yescharacteristic
366C22×D5—28no—
367C22×D5—28no—
368C22×D5—28no—
369C22×D5—28no—
370C22×D5—28no—
371C22×D5—28no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—28no—
377C22×D5—28no—
378C22×D5—28no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—22no—
385C22×D5—22no—
386C22×D5—22no—
387C22×D5—22no—
388C22×D5—22no—
389C22×D5—22no—
390C22×D5—22no—
391C22×D5—22no—
392C22×D5—44no—
393C22×D5—44no—
394C22×D5—44no—
395C22×D5—44no—
396C22×D5—44no—
397C22×D5—44no—
398C22×D5—44no—
399C22×D5—44no—
400C22×D5—44no—
401C22×D5—44no—
402C22×D5—44no—
403C22×D5#123116yescomplemented
404C22×D5C22×D414yes—
405C22×D5C22×D414yes—
406C22×D5C2×#4114yes—
407C22×D5C2×#4114yes—
408C2×C4×C5—28no—
409C2×C4×C5—28no—
410C2×C4×C5—28no—
411C2×C4×C5—28no—
412C2×C4×C5—22no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—22no—
416C2×C4×C5—22no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—22no—
423C2×C4×C5—22no—
424C2×C4×C5—22no—
425C2×C4×C5—22no—
426C2×C4×C5—22no—
427C2×C4×C5—22no—
428C2×C4×C5—22no—
429C2×C4×C5—44no—
430C2×C4×C5—44no—
431C2×C4×C5—44no—
432C2×C4×C5C22×D414yes—
433C2×C4×C5C22×D414yes—
434C2×C4×C5C22×D414yes—
435C2×C4×C5C22×D414yes—
436C2×Dic5—28no—
437C2×Dic5—22no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—22no—
441C2×Dic5—22no—
442C2×Dic5—22no—
443C2×Dic5—22no—
444C2×Dic5—22no—
445C2×Dic5—22no—
446C2×Dic5—22no—
447C2×Dic5—22no—
448C2×Dic5—22no—
449C2×Dic5—22no—
450C2×Dic5—22no—
451C2×Dic5—44no—
452C2×Dic5—44no—
453C2×Dic5—44no—
454C2×Dic5—44no—
455C2×Dic5C2×#4114yes—
456D20—232no—
457D20—416no—
458D20—416no—
459C4×D5—232no—
460C4×D5—416no—
461C4×D5—416no—
462C4×D5—416no—
463C25—51no—
464C25—51no—
465C25—51no—
466C22×D4—58no—
467C22×D4—54no—
468C22×D4—54no—
469C22×D4—54no—
470C22×D4—104no—
471C22×D4—104no—
472C22×D4—104no—
473C22×D4—104no—
474C22×D4—104no—
475C22×D4—104no—
476C22×D4—104no—
477C22×D4—202no—
478C23×C4—51no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—54no—
484C23×C4—54no—
485C23×C4—54no—
486C23×C4—54no—
487C23×C4—104no—
488C23×C4—104no—
489C23×C4—104no—
490C23×C4—104no—
491C23×C4—104no—
492C23×C4—104no—
493C23×C4—104no—
494C23×C4—104no—
495C23×C4—104no—
496C23×C4—202no—
497C23×C4—202no—
498C23×C4—202no—
499C23×C4C22×D511yescharacteristic
500C23×C4C22×D511yescharacteristic
501C23×C4C22×D511yescharacteristic
502C23×C4C22×D511yescharacteristic
503C23×C4C22×D511yescharacteristic
504C23×C4C22×D511yescharacteristic
505C23×C4C22×D511yescharacteristic
506#123—1032no—
507#121—1032no—
508C4×D4—1032no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—54no—
511C2×C4⋊C4—54no—
512C2×C4⋊C4—54no—
513C2×C4⋊C4—54no—
514C2×C4⋊C4—54no—
515C2×C4⋊C4—54no—
516C2×C4⋊C4—104no—
517C2×C4⋊C4—104no—
518C2×C4⋊C4—104no—
519C2×C4⋊C4—104no—
520C2×C4⋊C4—104no—
521C2×C4⋊C4—1032no—
522C2×C4⋊C4—202no—
523C2×C4⋊C4D2018yescomplemented
524C2×C4⋊C4C22×D514yes—
525C2×C4⋊C4C22×D514yes—
526C2×C22⋊C4—54no—
527C2×C22⋊C4—54no—
528C2×C22⋊C4—54no—
529C2×C22⋊C4—54no—
530C2×C22⋊C4—54no—
531C2×C22⋊C4—54no—
532C2×C22⋊C4—54no—
533C2×C22⋊C4—54no—
534C2×C22⋊C4—54no—
535C2×C22⋊C4—54no—
536C2×C22⋊C4—54no—
537C2×C22⋊C4—104no—
538C2×C22⋊C4—104no—
539C2×C22⋊C4—104no—
540C2×C22⋊C4—104no—
541C2×C22⋊C4—104no—
542C2×C22⋊C4—104no—
543C2×C22⋊C4—104no—
544C2×C22⋊C4—104no—
545C2×C22⋊C4—104no—
546C2×C22⋊C4—104no—
547C2×C22⋊C4—202no—
548C2×C42—24no—
549C2×C42C22×D514yes—
550#95—54no—
551#95—54no—
552#95—54no—
553#95—54no—
554#95C22×D514yes—
555#95C22×D514yes—
556#95C22×D514yes—
557#95C22×D514yes—
558C22×C5C2×#12314yes—
559C22×C5#52514yes—
560C22×C5#53914yes—
561C22×C5D4214yes—
562C22×C5#54714yes—
563C22×C5#54814yes—
564C22×C5#55314yes—
565C22×C5C23×D411yescharacteristic
566C22×C5C23×D411yescharacteristic
567C22×C5C22×#4111yescharacteristic
568C22×C5C22×#4111yescharacteristic
569C22×C5C22×#4111yescharacteristic
570C22×C5C2×H(5,𝔽2)11yescharacteristic
571C22×C5C2×2−1+411yescharacteristic
572C2×D5—24no—
573C2×D5—24no—
574C2×D5—24no—
575C2×D5—24no—
576C2×D5—24no—
577C2×D5—232no—
578C2×D5—24no—
579C2×D5—24no—
580C2×D5—24no—
581C2×D5—24no—
582C2×D5—42no—
583C2×D5—42no—
584C2×D5—42no—
585C2×D5—416no—
586C2×D5—42no—
587C2×D5—42no—
588C2×D5—42no—
589C2×D5—42no—
590C2×D5—42no—
591C2×D5—42no—
592C2×D5—42no—
593C2×D5—42no—
594C2×D5—88no—
595C2×D5C2×#12318yescomplemented
596C4×C5—24no—
597C4×C5—24no—
598C4×C5—24no—
599C4×C5—24no—
600C4×C5—42no—
601C4×C5—42no—
602C4×C5—42no—
603Dic5—24no—
604Dic5—42no—
605Dic5—42no—
606Dic5—42no—
607Dic5—42no—
608C24—54no—
609C24—54no—
610C24—54no—
611C24—52no—
612C24—54no—
613C24—52no—
614C24—52no—
615C24—102no—
616C24—102no—
617C24—102no—
618C24—102no—
619C24—102no—
620C24—102no—
621C24—102no—
622C24—102no—
623C24—102no—
624C24—102no—
625C24—102no—
626C24—102no—
627C24—102no—
628C24—102no—
629C24—102no—
630C24—102no—
631C24—102no—
632C24C23×D511yescharacteristic
633C2×D4—516no—
634C2×D4—1032no—
635C2×D4—108no—
636C2×D4—108no—
637C2×D4—108no—
638C2×D4—108no—
639C2×D4—108no—
640C2×D4—108no—
641C2×D4—108no—
642C2×D4—204no—
643C2×D4—2016no—
644C2×D4—2016no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—54no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—52no—
667C22×C4—52no—
668C22×C4—108no—
669C22×C4—108no—
670C22×C4—1032no—
671C22×C4—108no—
672C22×C4—108no—
673C22×C4—108no—
674C22×C4—102no—
675C22×C4—102no—
676C22×C4—108no—
677C22×C4—102no—
678C22×C4—102no—
679C22×C4—102no—
680C22×C4—102no—
681C22×C4—102no—
682C22×C4—102no—
683C22×C4—102no—
684C22×C4—102no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—108no—
690C22×C4—108no—
691C22×C4—108no—
692C22×C4—204no—
693C22×C4—204no—
694C22×C4—204no—
695C22×C4—2016no—
696C22×C4—2016no—
697C22×C4—2016no—
698C22×C4C2×D2014yes—
699C22×C4C2×D2014yes—
700C22×C4C2×D2014yes—
701C22×C4D4×D514yes—
702C22×C4C23×D512yes—
703C22×C4C23×D512yes—
704C22×C4C23×D512yes—
705C22×C4C23×D512yes—
706C22×C4C23×D512yes—
707C22×C4C23×D512yes—
708C22×C4C23×D512yes—
709C4⋊C4—28no—
710C4⋊C4—108no—
711C4⋊C4—108no—
712C4⋊C4—108no—
713C4⋊C4—108no—
714C4⋊C4—108no—
715C4⋊C4—204no—
716C4⋊C4C2×D20116yescomplemented
717C22⋊C4—108no—
718C22⋊C4—108no—
719C22⋊C4—108no—
720C22⋊C4—108no—
721C22⋊C4—108no—
722C22⋊C4—108no—
723C22⋊C4—108no—
724C22⋊C4—108no—
725C22⋊C4—108no—
726C22⋊C4—108no—
727C22⋊C4—204no—
728C42—28no—
729C2×C5#244318yescomplemented
730C2×C5C22×#12311yescharacteristic
731C2×C5C2×#52511yescharacteristic
732C2×C5C2×#53911yescharacteristic
733C2×C5C2×D4211yescharacteristic
734C2×C5C2×#54711yescharacteristic
735C2×C5C2×#54811yescharacteristic
736C2×C5C2×#55311yescharacteristic
737D5—28no—
738D5—44no—
739D5—82no—
740C23—516no—
741C23—54no—
742C23—54no—
743C23—54no—
744C23—54no—
745C23—108no—
746C23—108no—
747C23—108no—
748C23—108no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23—102no—
753C23—108no—
754C23—108no—
755C23—108no—
756C23—108no—
757C23—108no—
758C23—102no—
759C23—102no—
760C23—102no—
761C23—102no—
762C23—102no—
763C23—102no—
764C23—102no—
765C23—102no—
766C23—102no—
767C23—102no—
768C23—102no—
769C23—102no—
770C23—102no—
771C23—204no—
772C23—204no—
773C23—204no—
774C23—204no—
775C23—204no—
776C23—204no—
777C23—204no—
778C23—204no—
779C23—204no—
780C23—204no—
781C23—204no—
782C23C22×D2012yes—
783C23C2×D4×D512yes—
784C23#414712yes—
785C23D5×#4112yes—
786C23D5×#4112yes—
787C23D5×#4112yes—
788C23#414912yes—
789C23C24×D511yescharacteristic
790D4—1032no—
791D4—2016no—
792D4—2016no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—54no—
818C2×C4—1032no—
819C2×C4—108no—
820C2×C4—102no—
821C2×C4—102no—
822C2×C4—102no—
823C2×C4—102no—
824C2×C4—102no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—102no—
832C2×C4—102no—
833C2×C4—102no—
834C2×C4—2016no—
835C2×C4—2016no—
836C2×C4—2016no—
837C2×C4—204no—
838C2×C4—204no—
839C2×C4—204no—
840C2×C4—204no—
841C2×C4C22×D2014yes—
842C2×C4C22×D2014yes—
843C2×C4C22×D2014yes—
844C2×C4C2×D4×D514yes—
845C5C2×#244311yescharacteristic, complemented, Sylow
846C22—58no—
847C22—104no—
848C22—104no—
849C22—104no—
850C22—104no—
851C22—104no—
852C22—104no—
853C22—1032no—
854C22—104no—
855C22—104no—
856C22—104no—
857C22—202no—
858C22—202no—
859C22—202no—
860C22—202no—
861C22—2016no—
862C22—202no—
863C22—202no—
864C22—202no—
865C22—202no—
866C22—202no—
867C22—202no—
868C22—202no—
869C22—408no—
870C22#6585814yes—
871C22D4×D2014yes—
872C22#6591014yes—
873C22#6596514yes—
874C22D5×#12314yes—
875C22#6602614yes—
876C22#6604314yes—
877C22C23×D2011yescharacteristic
878C22C22×D4×D511yescharacteristic
879C22C2×#414711yescharacteristic
880C22C2×D5×#4111yescharacteristic
881C22C2×D5×#4111yescharacteristic
882C22C2×D5×#4111yescharacteristic
883C22C2×#414911yescharacteristic
884C4—24no—
885C4—24no—
886C4—24no—
887C4—24no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—104no—
892C4—202no—
893C4—202no—
894C4—202no—
895C4—202no—
896C2—108no—
897C2—204no—
898C2—402no—
899C2#1060705018yesdirect product factor
900C2C2×#6585811yescharacteristic
901C2C2×D4×D2011yescharacteristic
902C2C2×#6591011yescharacteristic
903C2C2×#6596511yescharacteristic
904C2C2×D5×#12311yescharacteristic
905C2C2×#6602611yescharacteristic
906C2C2×#6604311yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC2×C5×#387C2
socleC24×C5C24
prime radicalC22×#4041C2
hypercenterC2×#387D5
hypocenterC5C2×#2443
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×#387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#4040C2semidirect
3. C22×D5×C4⋊C4C2semidirect
4. C22×C4×D20C2semidirect
5. C2×C5×#387C2semidirect
6. C2×#65272C2semidirect
7. C2×#65229C2semidirect
8. #10607050C2direct (N × H)
9. C2×#64966C2semidirect
10. C2×#64954C2semidirect
11. C2×#64954C2semidirect
12. C2×#64954C2semidirect
13. C2×#64957C2semidirect
14. C2×#64957C2semidirect
15. C2×#64963C2semidirect
16. C2×#64961C2semidirect
47. C2×#4040C22semidirect
49. C2×D5×C4⋊C4C22semidirect
51. C2×C4×D20C22semidirect
52. C5×#387C22semidirect
61. #65272C22semidirect
62. #65229C22semidirect
63. #64966C22semidirect
64. #64963C22semidirect
65. #64961C22semidirect
66. #64957C22semidirect
67. #64957C22semidirect
68. #64954C22semidirect
69. #64954C22semidirect
70. #64954C22semidirect
116. C2×C5×C4⋊C4D4semidirect
177. C2×#387D5semidirect
285. C5×C4⋊C4C2×D4semidirect
344. #387C2×D5semidirect
403. C22×D5#123semidirect
523. C2×C4⋊C4D20semidirect
595. C2×D5C2×#123semidirect
716. C4⋊C4C2×D20semidirect
729. C2×C5#2443semidirect
845. C5C2×#2443semidirect
899. C2#10607050direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#40402
C22×#40412
C22×D5×C4⋊C42
C22×C4×D202
C2×C5×#3872
C2×#652722
C2×#652292
#106070502
C2×#649662
C2×#649542
C2×#649572
C2×#649632
C2×#649612
C2×#24435